Aether has mass

'Empty Black Holes, Firewalls, and the Origin of Bekenstein-Hawking
Entropy'
http://arxiv.org/abs/1212.4176

"But why an incompressible fluid? The reason comes from an attempt to
solve the (old) cosmological constant problem, which is arguably the
most puzzling aspect of coupling gravity to relativistic quantum
mechanics [13]. Given that the natural expectation value for the
vacuum of the standard model of particle physics is ∼ 60 orders of
magnitude heavier than the gravitational measurements of vacuum
density, it is reasonable to entertain an alternative theory of
gravity where the standard model vacuum decouples from gravity. Such a
theory could be realized by coupling gravity to the traceless part of
the quantum mechanical energy-momentum tensor. However, the
consistency/covariance of gravitational field equations then requires
introducing an auxiliary fluid, the so-called gravitational aether
[14]. The simplest model for gravitational aether is an incompressible
fluid (with vanishing energy density, but non-vanishing pressure),
which is currently consistent with all cosmological, astrophysical,
and precision tests of gravity [15, 16]:

Gμν = Tμν − Tα gμν + Tμν ,
Tμν = p (uμ uν + gμν ), T μν;ν = 0, (1)

where GN is Newton’s constant, Tμν is the matter energy momentum
tensor and Tμν is the incompressible gravitational aether fluid. In
vacuum, the theory reduces to GR coupled to an incompressible fluid."